The bishops say the Refugee Program Integrity Restoration Act would "roll back protections for refugees seeking admission to the United States, as well as for refugees who have already been admitted to the country."
They call for everyone who supports refugee resettlement to speak out against the bill. "We must persuade them to not bring this dangerous measure to a vote in the full House of Representatives."
The House judiciary committee approved the legislation last month.
If brought to a vote and passed, it would drastically reduce and cap refugee admissions and give Congress rather than the President the authority to set annual levels of refugee admissions.
Refugees would be placed under continual surveillance after arrival.
The bishops also say the bill would "significantly and potentially indefinitely delay resettlement for many refugees whose lives are in danger."
This would affect Central Americans, Syrians, Iraqis and others.
The bishops also say the bill seeks to elevate religious persecution above all other grounds, and then seeks to favor "particular religions" over others for priority consideration.
The bishops are urging Catholics to email the speaker Paul Ryan and majority leader Kevin McCarthy. They say that in the face of the refugee crisis, resettlement is one of three "durable solutions".
As a global leader, they say, it is critical the US keeps its doors open to encourage other countries to do the same.
They cite Albert Einstein, Henry Kissinger, Madeleine Albright and Sergey Brin, the founder of Google, as former refugees whose accomplishments demonstrate what the US has to gain from welcoming refugees.